Question

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In ΔABC, the bisectors of ∠ABC and ∠BCA intersect each other at O. The measure of ∠BOC is​

Answer 1

Answer:

Step-by-step explanation:

Sum of angles of a triangle is 180°.

Angle bisector divided angle in two equal half

In ΔABC

∠A + ∠B + ∠C  = 180°

=> ∠B + ∠C  = 180° - ∠A  Eq1

bisectors of ∠ABC and ∠BCA intersect each other at O.

=> ∠OBC = (1/2) ∠B     and  ∠OCB =  (1/2)∠C

in ΔOBC

∠OBC  + ∠OCB +  ∠BOC = 180°

=> (1/2) ∠B + (1/2)∠C  + ∠BOC = 180°

=> (1/2) ( ∠B + ∠C) + ∠BOC = 180°

From Eq1  ∠B + ∠C  = 180° - ∠A

=> (1/2) (  180° - ∠A) + ∠BOC = 180°

=> 90° - ∠A/2  + ∠BOC = 180°

=> ∠BOC = 180° - 90° + ∠A/2

=> ∠BOC =  90° + ∠A/2

The measure of ∠BOC is  90° + ∠A/2